%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET009^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:23:09 AM UTC 2026
% Result : Theorem 0.12s 0.25s
% Output : Refutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 12
% Syntax : Number of formulae : 70 ( 23 unt; 0 typ; 11 def)
% Number of atoms : 284 ( 86 equ; 0 cnn)
% Maximal formula atoms : 6 ( 4 avg)
% Number of connectives : 248 ( 67 ~; 47 |; 22 &; 91 @)
% ( 6 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 24 ( 24 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 16 usr; 12 con; 0-2 aty)
% Number of variables : 49 ( 0 sgn 37 !; 12 ?; 49 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_3,type,
sK0: a > $o ).
thf(func_def_4,type,
sK1: a > $o ).
thf(func_def_5,type,
sK2: a > $o ).
thf(func_def_6,type,
sK3: a ).
thf(func_def_7,type,
sF4: $o ).
thf(func_def_8,type,
sF5: $o ).
thf(func_def_9,type,
sF6: $o ).
thf(func_def_10,type,
sF7: a > $o ).
thf(func_def_11,type,
sF8: a > $o ).
thf(f1,conjecture,
! [X2: a > $o,X0: a > $o,X1: a > $o] :
( ! [X3: a] :
( ( X0 @ X3 )
=> ( X1 @ X3 ) )
=> ! [X3: a] :
( ( ~ ( X1 @ X3 )
& ( X2 @ X3 ) )
=> ( ~ ( X0 @ X3 )
& ( X2 @ X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cBOOL_PROP_47_pme) ).
thf(f2,negated_conjecture,
~ ! [X2: a > $o,X0: a > $o,X1: a > $o] :
( ! [X3: a] :
( ( X0 @ X3 )
=> ( X1 @ X3 ) )
=> ! [X3: a] :
( ( ~ ( X1 @ X3 )
& ( X2 @ X3 ) )
=> ( ~ ( X0 @ X3 )
& ( X2 @ X3 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ! [X3: a] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) )
=> ! [X4: a] :
( ( ~ ( X2 @ X4 )
& ( X0 @ X4 ) )
=> ( ~ ( X1 @ X4 )
& ( X0 @ X4 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ! [X3: a] :
( ( ( X1 @ X3 )
= $true )
=> ( ( X2 @ X3 )
= $true ) )
=> ! [X4: a] :
( ( ( ( X2 @ X4 )
!= $true )
& ( $true
= ( X0 @ X4 ) ) )
=> ( ( $true
!= ( X1 @ X4 ) )
& ( $true
= ( X0 @ X4 ) ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
~ ! [X2: a > $o,X1: a > $o,X0: a > $o] :
( ! [X3: a] :
( ( ( X1 @ X3 )
= $true )
=> ( ( X2 @ X3 )
= $true ) )
=> ! [X4: a] :
( ( ( ( X2 @ X4 )
!= $true )
& ( $true
= ( X0 @ X4 ) ) )
=> ( ( $true
!= ( X1 @ X4 ) )
& ( $true
= ( X0 @ X4 ) ) ) ) ),
inference(flattening,[],[f4]) ).
thf(f6,plain,
? [X2: a > $o,X1: a > $o,X0: a > $o] :
( ? [X4: a] :
( ( ( $true
= ( X1 @ X4 ) )
| ( $true
!= ( X0 @ X4 ) ) )
& ( ( X2 @ X4 )
!= $true )
& ( $true
= ( X0 @ X4 ) ) )
& ! [X3: a] :
( ( ( X1 @ X3 )
!= $true )
| ( ( X2 @ X3 )
= $true ) ) ),
inference(ennf_transformation,[],[f5]) ).
thf(f7,plain,
? [X0: a > $o,X2: a > $o,X1: a > $o] :
( ? [X4: a] :
( ( $true
= ( X0 @ X4 ) )
& ( ( $true
= ( X1 @ X4 ) )
| ( $true
!= ( X0 @ X4 ) ) )
& ( ( X2 @ X4 )
!= $true ) )
& ! [X3: a] :
( ( ( X1 @ X3 )
!= $true )
| ( ( X2 @ X3 )
= $true ) ) ),
inference(flattening,[],[f6]) ).
thf(f8,plain,
? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ? [X3: a] :
( ( ( X0 @ X3 )
= $true )
& ( ( ( X2 @ X3 )
= $true )
| ( ( X0 @ X3 )
!= $true ) )
& ( ( X1 @ X3 )
!= $true ) )
& ! [X4: a] :
( ( ( X2 @ X4 )
!= $true )
| ( $true
= ( X1 @ X4 ) ) ) ),
inference(rectify,[],[f7]) ).
thf(f9,plain,
( ( ( sK0 @ sK3 )
= $true )
& ( ( $true
= ( sK2 @ sK3 ) )
| ( ( sK0 @ sK3 )
!= $true ) )
& ( ( sK1 @ sK3 )
!= $true )
& ! [X4: a] :
( ( ( sK2 @ X4 )
!= $true )
| ( $true
= ( sK1 @ X4 ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f8]) ).
thf(f10,plain,
! [X4: a] :
( ( ( sK2 @ X4 )
!= $true )
| ( $true
= ( sK1 @ X4 ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f11,plain,
( ( sK1 @ sK3 )
!= $true ),
inference(cnf_transformation,[],[f9]) ).
thf(f12,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( ( sK0 @ sK3 )
!= $true ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f13,plain,
( ( sK0 @ sK3 )
= $true ),
inference(cnf_transformation,[],[f9]) ).
thf(f16,definition,
( sF4
= ( sK0 @ sK3 ) ),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
thf(f17,plain,
sF4 = $true,
inference(definition_folding,[],[f13,f16]) ).
thf(f18,definition,
( sF5
= ( sK2 @ sK3 ) ),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
thf(f19,plain,
( ( sK2 @ sK3 )
= sF5 ),
inference(reorient_equations,[],[f18]) ).
thf(f20,plain,
( ( sF4 != $true )
| ( $true = sF5 ) ),
inference(definition_folding,[],[f12,f16,f19]) ).
thf(f21,definition,
( sF6
= ( sK1 @ sK3 ) ),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
thf(f22,plain,
( ( sK1 @ sK3 )
= sF6 ),
inference(reorient_equations,[],[f21]) ).
thf(f23,plain,
$true != sF6,
inference(definition_folding,[],[f11,f22]) ).
thf(f24,definition,
! [X4: a] :
( ( sF7 @ X4 )
= ( sK2 @ X4 ) ),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
thf(f25,plain,
! [X4: a] :
( ( sK2 @ X4 )
= ( sF7 @ X4 ) ),
inference(reorient_equations,[],[f24]) ).
thf(f26,definition,
! [X4: a] :
( ( sF8 @ X4 )
= ( sK1 @ X4 ) ),
introduced(definition,[new_symbols(definition,[sF8])],[function_definition]) ).
thf(f27,plain,
! [X4: a] :
( ( sK1 @ X4 )
= ( sF8 @ X4 ) ),
inference(reorient_equations,[],[f26]) ).
thf(f28,plain,
! [X4: a] :
( ( $true
= ( sF8 @ X4 ) )
| ( $true
!= ( sF7 @ X4 ) ) ),
inference(definition_folding,[],[f10,f27,f25]) ).
thf(f29,plain,
! [X4: a] :
( ( $true
= ( sK1 @ X4 ) )
| ( $false
= ( sF8 @ X4 ) ) ),
inference(iff_proxy_clausification,[],[f27]) ).
thf(f31,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $false = sF5 ) ),
inference(iff_proxy_clausification,[],[f19]) ).
thf(f34,plain,
! [X4: a] :
( ( $true
= ( sF7 @ X4 ) )
| ( $false
= ( sK2 @ X4 ) ) ),
inference(iff_proxy_clausification,[],[f25]) ).
thf(f38,plain,
( ( $true = sF6 )
| ( $false
= ( sK1 @ sK3 ) ) ),
inference(iff_proxy_clausification,[],[f22]) ).
thf(f40,definition,
( spl9_1
<=> ( $true = sF5 ) ),
introduced(definition,[new_symbols(definition,[spl9_1])],[avatar_definition]) ).
thf(f42,plain,
( ( $true = sF5 )
| ~ spl9_1 ),
inference(avatar_component_clause,[],[f40]) ).
thf(f44,definition,
( spl9_2
<=> ( sF4 = $true ) ),
introduced(definition,[new_symbols(definition,[spl9_2])],[avatar_definition]) ).
thf(f47,plain,
( spl9_1
| ~ spl9_2 ),
inference(avatar_split_clause,[],[f20,f44,f40]) ).
thf(f54,definition,
( spl9_4
<=> ( $true
= ( sK2 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl9_4])],[avatar_definition]) ).
thf(f56,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ~ spl9_4 ),
inference(avatar_component_clause,[],[f54]) ).
thf(f58,definition,
( spl9_5
<=> ( $false = sF5 ) ),
introduced(definition,[new_symbols(definition,[spl9_5])],[avatar_definition]) ).
thf(f60,plain,
( ( $false = sF5 )
| ~ spl9_5 ),
inference(avatar_component_clause,[],[f58]) ).
thf(f61,plain,
( spl9_4
| spl9_5 ),
inference(avatar_split_clause,[],[f31,f58,f54]) ).
thf(f62,plain,
spl9_2,
inference(avatar_split_clause,[],[f17,f44]) ).
thf(f78,definition,
( spl9_9
<=> ( $false
= ( sK1 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl9_9])],[avatar_definition]) ).
thf(f80,plain,
( ( $false
= ( sK1 @ sK3 ) )
| ~ spl9_9 ),
inference(avatar_component_clause,[],[f78]) ).
thf(f82,definition,
( spl9_10
<=> ( $true = sF6 ) ),
introduced(definition,[new_symbols(definition,[spl9_10])],[avatar_definition]) ).
thf(f85,plain,
( spl9_9
| spl9_10 ),
inference(avatar_split_clause,[],[f38,f82,f78]) ).
thf(f95,plain,
~ spl9_10,
inference(avatar_split_clause,[],[f23,f82]) ).
thf(f116,plain,
( ( $false = $true )
| ( $false
= ( sF8 @ sK3 ) )
| ~ spl9_9 ),
inference(constrained_superposition,[],[f80,f29]) ).
thf(f117,plain,
( ( $false
= ( sF8 @ sK3 ) )
| ~ spl9_9 ),
inference(trivial_inequality_removal,[],[f116]) ).
thf(f121,plain,
( ( $false = $true )
| ( ( sF7 @ sK3 )
!= $true )
| ~ spl9_9 ),
inference(constrained_superposition,[],[f28,f117]) ).
thf(f123,plain,
( ( ( sF7 @ sK3 )
!= $true )
| ~ spl9_9 ),
inference(trivial_inequality_removal,[],[f121]) ).
thf(f140,plain,
( ( $true != $true )
| ( $false
= ( sK2 @ sK3 ) )
| ~ spl9_9 ),
inference(constrained_superposition,[],[f123,f34]) ).
thf(f145,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ~ spl9_9 ),
inference(trivial_inequality_removal,[],[f140]) ).
thf(f153,plain,
( ( $false = $true )
| ~ spl9_4
| ~ spl9_9 ),
inference(forward_demodulation,[],[f145,f56]) ).
thf(f154,plain,
( $false
| ~ spl9_4
| ~ spl9_9 ),
inference(trivial_inequality_removal,[],[f153]) ).
thf(f155,plain,
( ~ spl9_4
| ~ spl9_9 ),
inference(avatar_contradiction_clause,[],[f154]) ).
thf(f157,plain,
( ( $false = $true )
| ~ spl9_1
| ~ spl9_5 ),
inference(forward_demodulation,[],[f60,f42]) ).
thf(f158,plain,
( $false
| ~ spl9_1
| ~ spl9_5 ),
inference(trivial_inequality_removal,[],[f157]) ).
thf(f159,plain,
( ~ spl9_1
| ~ spl9_5 ),
inference(avatar_contradiction_clause,[],[f158]) ).
cnf(s1,plain,
( spl9_1
| ~ spl9_2 ),
inference(sat_conversion,[],[f47]) ).
cnf(s3,plain,
( spl9_4
| spl9_5 ),
inference(sat_conversion,[],[f61]) ).
cnf(s4,plain,
spl9_2,
inference(sat_conversion,[],[f62]) ).
cnf(s7,plain,
( spl9_9
| spl9_10 ),
inference(sat_conversion,[],[f85]) ).
cnf(s9,plain,
~ spl9_10,
inference(sat_conversion,[],[f95]) ).
cnf(s14,plain,
( ~ spl9_4
| ~ spl9_9 ),
inference(sat_conversion,[],[f155]) ).
cnf(s16,plain,
( ~ spl9_1
| ~ spl9_5 ),
inference(sat_conversion,[],[f159]) ).
cnf(s20,plain,
spl9_9,
inference(rat,[],[s7,s9]) ).
cnf(s22,plain,
~ spl9_4,
inference(rat,[],[s14,s20]) ).
cnf(s24,plain,
spl9_5,
inference(rat,[],[s3,s22]) ).
cnf(s25,plain,
~ spl9_1,
inference(rat,[],[s16,s24]) ).
cnf(s26,plain,
$false,
inference(rat,[],[s1,s4,s25]) ).
thf(f160,plain,
$false,
inference(avatar_sat_refutation,[],[s26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET009^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.17 % Computer : n009.cluster.edu
% 0.12/0.17 % Model : x86_64 x86_64
% 0.12/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.17 % Memory : 8046.5625MB
% 0.12/0.17 % OS : Linux 6.8.0-71-generic
% 0.12/0.17 % CPULimit : 300
% 0.12/0.17 % WCLimit : 300
% 0.12/0.17 % DateTime : Tue Sep 29 13:35:23 UTC 2026
% 0.12/0.17 % CPUTime :
% 0.12/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.20 Running higher-order theorem proving
% 0.12/0.21 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.25 % (3990698)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.12/0.25 % (3990709)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.12/0.25 % (3990709)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.12/0.25 % (3990709)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=2507286080:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.12/0.25 % (3990709) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3990698-3990709"...
% 0.12/0.25 % (3990709)...printing done.
% 0.12/0.25 % (3990709)Refutation found. Thanks to Tanya!
% 0.12/0.25 % SZS status Theorem for theBenchmark
% 0.12/0.25 % SZS output start Proof for theBenchmark
% See solution above
% 0.12/0.25 % (3990709)------------------------------
% 0.12/0.25 % (3990709)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.12/0.25 % (3990709)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.12/0.25 % (3990709)CaDiCaL version: 2.1.3
% 0.12/0.25 % (3990709)Termination reason: Refutation
% 0.12/0.25 % (3990709)Time elapsed: 0.002 s
% 0.12/0.25 % (3990709)Peak memory usage: 13 MB
% 0.12/0.25 % (3990709)Instructions burned: 5 (million)
% 0.12/0.25 % (3990698)Success in time 0.033 s
% 0.12/0.25 % Vampire exiting
%------------------------------------------------------------------------------